Question: Stephanie is 2 times as old as Umaima. Twenty years ago, Stephanie was 6 times as old as Umaima. How old is Stephanie now?
Answer: We can use the given information to write down two equations that describe the ages of Stephanie and Umaima. Let Stephanie's current age be $s$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $s = 2u$ Twenty years ago, Stephanie was $s - 20$ years old, and Umaima was $u - 20$ years old. The information in the second sentence can be expressed in the following equation: $s - 20 = 6(u - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to solve our first equation for $u$ and substitute it into our second equation. Solving our first equation for $u$ , we get: $u = s / 2$ . Substituting this into our second equation, we get: $s - 20 = 6($ $(s / 2)$ $- 20)$ which combines the information about $s$ from both of our original equations. Simplifying the right side of this equation, we get: $s - 20 = 3 s - 120$ Solving for $s$ , we get: $2 s = 100$ $s = \dfrac{1}{2} \cdot 100 = 50$.